USA Today reports (Gary Stoller, “Hotel Bill Mistakes Mean Many Pay Too Much”) that George Hansen, CEO of Wichita-based Corporate Lodging Consultants, conducted a recent review of hotel bills over a 12-month period. The review indicated that, on average, errors in hotel bills resulted in overpayment of $11.35 per night. To determine if such mistakes are being made at a major hotel chain, the CEO might direct a survey yielding the following data:

The file OverPay contains these data.
a. Conduct a hypothesis test with α = 0.05 to determine if the average overpayment is smaller than that indicated by Corporate Lodging Consultants.
b. If the actual average overpayment at the hotel chain was $11 with an actual standard deviation of $1.50, determine the probability that the hypothesis test would correctly indicate that the actual average is less than $11.35.